Brownian motion of arbitrarily shaped particles in two dimensions

Dynamics of wire frame glasses in two dimensions

The dynamics of wire frame particles in concentrated suspension are studied by means of a 2D model and compared to those of rod-like particles. The wire frames have bent or branched structures constructed from infinitely thin, rigid rods. In the model, a particle is surrounded by diffusing points that it cannot cross. We derive a formal expression for the mean squared displacement (MSD) and, by using a self-consistent approximation, we find markedly different dynamics for wire frames and rods. For wire frames, there exists a critical concentration of points above which they become frozen with the long time MSD reaching a plateau. Rods, on the other hand, always diffuse by reptation. We also study the rheology through the elastic stress, and more striking differences are found: the initial magnitude of the stress for wire frames is much larger than for rods, scaling such as the square of the point concentration, and above the critical concentration, the stress for wire frames appears to persist indefinitely while for rods it always decays.

3-D rotation tracking from 2-D images of spherical colloids with textured surfaces

Tracking the three-dimensional rotation of colloidal particles is essential to elucidate many open questions, e.g. concerning the contact interactions between particles under flow, or the way in which obstacles and neighboring particles affect self-propulsion in active suspensions. In order to achieve rotational tracking, optically anisotropic particles are required. We synthesise here rough spherical colloids that present randomly distributed fluorescent asperities and track their motion under different experimental conditions. Specifically, we propose a new algorithm based on a 3-D rotation registration, which enables us to track the 3-D rotation of our rough colloids at short time-scales, using time series of 2-D images acquired at high frame rates with a conventional wide-field microscope. The method is based on the image correlation between a reference image and rotated 3-D prospective images to identify the most likely angular displacements between frames. We first validate our approach against simulated data and then apply it to the cases of: particles flowing through a capillary, freely diffusing at solid-liquid and liquid-liquid interfaces, and self-propelling above a substrate. By demonstrating the applicability of our algorithm and sharing the code, we hope to encourage further investigations in the rotational dynamics of colloidal systems.

Effect of curvature on the diffusion of colloidal bananas

Anisotropic colloidal particles exhibit complex dynamics which play a crucial role in their functionality, transport, and phase behavior. In this Letter, we investigate the two-dimensional diffusion of smoothly curved colloidal rods-also known as colloidal bananas-as a function of their opening angle α. We measure the translational and rotational diffusion coefficients of the particles with opening angles ranging from 0^{∘} (straight rods) to nearly 360^{∘}(closed rings). In particular, we find that the anisotropic diffusion of the particles varies nonmonotonically with their opening angle and that the axis of fastest diffusion switches from the long to the short axis of the particles when α>180^{∘}. We also find that the rotational diffusion coefficient of nearly closed rings is approximately an order of magnitude higher than that of straight rods of the same length. Finally, we show that the experimental results are consistent with slender body theory, indicating that the dynamical behavior of the particles arises primarily from their local drag anisotropy. These results highlight the impact of curvature on the Brownian motion of elongated colloidal particles, which must be taken into account when seeking to understand the behavior of curved colloidal particles.

Inertial dynamics of an active Brownian particle

Active Brownian motion commonly assumes spherical overdamped particles. However, self-propelled particles are often neither symmetric nor overdamped yet underlie random fluctuations from their surroundings. Active Brownian motion has already been generalized to include asymmetric particles. Separately, recent findings have shown the importance of inertial effects for particles of macroscopic size or in low-friction environments. We aim to consolidate the previous findings into the general description of a self-propelled asymmetric particle with inertia. We derive the Langevin equation of such a particle as well as the corresponding Fokker-Planck equation. Furthermore, a formula is presented that allows reconstructing the hydrodynamic resistance matrix of the particle by measuring its trajectory. Numerical solutions of the Langevin equation show that, independently of the particle's shape, the noise-free trajectory at zero temperature starts with an inertial transition phase and converges to a circular helix. We discuss this universal convergence with respect to the helical motion that many microorganisms exhibit.

Probing Diffusive Dynamics of Natural Tubule Nanoclays with Machine Learning

Reproducibility of the experimental results and object of study itself is one of the basic principles in science. But what if the object characterized by technologically important properties is natural and cannot be artificially reproduced one-to-one in the laboratory? The situation becomes even more complicated when we are interested in exploring stochastic properties of a natural system and only a limited set of noisy experimental data is available. In this paper we address these problems by exploring diffusive motion of some natural clays, halloysite and sepiolite, in a liquid environment. By using a combination of dark-field microscopy and machine learning algorithms, a quantitative theoretical characterization of the nanotubes' rotational diffusive dynamics is performed. Scanning the experimental video with the gradient boosting tree method, we can trace time dependence of the diffusion coefficient and probe different regimes of nonequilibrium rotational dynamics that are due to contacts with surfaces and other experimental imperfections. The method we propose is of general nature and can be applied to explore diffusive dynamics of various biological systems in real time.

Two-dimensional Brownian motion of anisotropic dimers

We study the two-dimensional motion of colloidal dimers by single-particle tracking and compare the experimental observations obtained by bright-field microscopy to theoretical predictions for anisotropic diffusion. The comparison is based on the mean-square displacements in the laboratory and particle frame as well as generalizations of the self-intermediate scattering functions, which provide insights into the rotational dynamics of the dimer. The diffusional anisotropy leads to a measurable translational-rotational coupling that becomes most prominent by aligning the coordinate system with the initial orientation of the particles. In particular, we find a splitting of the time-dependent diffusion coefficients parallel and perpendicular to the long axis of the dimer which decays over the orientational relaxation time. Deviations of the self-intermediate scattering functions from pure exponential relaxation are small but can be resolved experimentally. The theoretical predictions and experimental results agree quantitatively.

Anisotropic diffusion of membrane proteins at experimental timescales

Single-particle tracking (SPT) experiments of lipids and membrane proteins provide a wealth of information about the properties of biomembranes. Careful analysis of SPT trajectories can reveal deviations from ideal Brownian behavior. Among others, this includes confinement effects and anomalous diffusion, which are manifestations of both the nanoscale structure of the underlying membrane and the structure of the diffuser. With the rapid increase in temporal and spatial resolution of experimental methods, a new aspect of the motion of the particle, namely, anisotropic diffusion, might become relevant. This aspect that so far received only little attention is the anisotropy of the diffusive motion and may soon provide an additional proxy to the structure and topology of biomembranes. Unfortunately, the theoretical framework for detecting and interpreting anisotropy effects is currently scattered and incomplete. Here, we provide a computational method to evaluate the degree of anisotropy directly from molecular dynamics simulations and also point out a way to compare the obtained results with those available from SPT experiments. In order to probe the effects of anisotropic diffusion, we performed coarse-grained molecular dynamics simulations of peripheral and integral membrane proteins in flat and curved bilayers. In agreement with the theoretical basis, our computational results indicate that anisotropy can persist up to the rotational relaxation time [τ=(2D_r)^-1], after which isotropic diffusion is observed. Moreover, the underlying topology of the membrane bilayer can couple with the geometry of the particle, thus extending the spatiotemporal domain over which this type of motion can be detected.

Helicoidal dynamics of biaxial curved rods in twist-bend nematic phases unveiled by unsupervised machine learning techniques

Uniaxial rods in a nematic phase diffuse preferentially in the direction parallel to the nematic director n[over ̂]. The nematic director field n[over ̂](r) of a chiral twist-bend nematic (N_{TB}) phase of achiral banana-shaped particles, recently discovered experimentally, displays a heliconical twist of given handedness and periodicity. Using simulations, we investigate the long-time macroscopic diffusion in N_{TB} phases, and find that the predilection of curved rods to diffuse in the direction of the twisting n[over ̂](r) yields a fascinating chiral dynamics along helices, even though achiral curved rods display Brownian motion with a nontrivial rototranslational coupling. We devise a machine learning protocol to characterize the helicoidal particle trajectories, finding that their pitch and radius are determined by the pitch and conical angle of the N_{TB} phase thereby connecting its structural and dynamical properties.

Different-shaped micro-objects driven by active particle aggregations

The dynamics of passive micro-objects in an active bath has been receiving much attention. However, the influence of the shapes of micro-objects remains unclear. Here, we use 2D simulation to investigate the interaction between active Brownian particles and different-shaped passive micro-objects. We show that active particles accumulate around micro-objects and self-assemble into living aggregations at a high active velocity and high volume fraction. The shapes of micro-objects affect the distributions of the aggregations. In turn, the different distribution of aggregations influences the motion of micro-objects and induces abnormal diffusive behaviors. We further demonstrate that polar distributed aggregations at a high active velocity and the inhibition of the active bath at a low active velocity induce the counterintuitive anisotropic enhanced diffusion of rods, and the steric interaction between active particles induces the reverse translation-rotation coupled diffusion of chevrons.

Mesoscopic simulations of anisotropic chemically powered nanomotors

Chemically powered self-propelled colloids generate a motor force by converting locally a source of energy into directed motion, a process that has been explored both in experiments and in computational models. The use of active colloids as building blocks for nanotechnology opens the doors to interesting applications, provided we understand the behavior of these elementary constituents. We build a consistent mesoscopic simulation model for self-propelled colloids of complex shape with the aim of resolving the coupling between their translational and rotational motion. Considering a passive L-shaped colloidal particle, we study its Brownian dynamics and locate its center of hydrodynamics, the tracking point at which translation and rotation decouple. The active L particle displays the same circling trajectories that have been found experimentally, a result which we compare with the Brownian dynamics model. We put forward the role of hydrodynamics by comparing our results with a fluid model in which the particles' velocities are reset randomly. There, the trajectories only display random orientations. We obtain these original simulation results without any parametrization of the algorithm, which makes it a useful method for the preliminary study of active colloids, prior to experimental work.

Brownian dynamics of fully confined suspensions of rigid particles without Green's functions

We introduce a Rigid-Body Fluctuating Immersed Boundary (RB-FIB) method to perform large-scale Brownian dynamics simulations of suspensions of rigid particles in fully confined domains, without any need to explicitly construct Green's functions or mobility operators. In the RB-FIB approach, discretized fluctuating Stokes equations are solved with prescribed boundary conditions in conjunction with a rigid-body immersed boundary method to discretize arbitrarily shaped colloidal particles with no-slip or active-slip prescribed on their surface. We design a specialized Split-Euler-Maruyama temporal integrator that uses a combination of random finite differences to capture the stochastic drift appearing in the overdamped Langevin equation. The RB-FIB method presented in this work only solves mobility problems in each time step using a preconditioned iterative solver and has a computational complexity that scales linearly in the number of particles and fluid grid cells. We demonstrate that the RB-FIB method correctly reproduces the Gibbs-Boltzmann equilibrium distribution and use the method to examine the time correlation functions for two spheres tightly confined in a cuboid. We model a quasi-two-dimensional colloidal crystal confined in a narrow microchannel and hydrodynamically driven across a commensurate periodic substrate potential mimicking the effect of a corrugated wall. We observe partial and full depinning of the colloidal monolayer from the substrate potential above a certain wall speed, consistent with a transition from static to kinetic friction through propagating kink solitons. Unexpectedly, we find that particles nearest to the boundaries of the domain are the first to be displaced, followed by particles in the middle of the domain.

Coupling and decoupling between translational and rotational dynamics in supercooled monodisperse soft Janus particles

We perform dynamics simulations to investigate the translational and rotational glassy dynamics in a glass-forming liquid of monodisperse soft Janus particles. We find that, with decreasing temperature, the mean-square angular displacement shows no clear plateau in the caging region, in contrast with the apparent caging behavior of translational motion. By defining a reorientational mean-square angular displacement, the caging behavior of rotational motion can be recognized. On approaching the glass transition (decreasing temperature), the coupling between translational and rotational relaxation increases, while the coupling between translational and rotational diffusion decreases, whereas the coupling between translational and reorientational diffusion increases. The strong decoupling between translational and rotational diffusion is due to the suppressed translational mobility but promoted rotational mobility of soft Janus particles. We think that the low-T SE and SED decoupling is mainly attributed to hopping motion of soft Janus particles, whereas the high-T SE and SED decoupling is mainly attributed to collective cage motion of soft Janus particles. Our results demonstrate that interaction anisotropy has a critical effect on the translational and rotational dynamics of soft Janus particles.

Experimental Assessment and Model Validation on How Shape Determines Sedimentation and Diffusion of Colloidal Particles

Understanding the hydrodynamics of colloids with complex shapes is of equal importance to widespread practical applications and fundamental scientific problems, such as gelation, crystallization, and phase behavior. Building on previous work, we present a comprehensive study of sedimentation, diffusion, intrinsic viscosities, and other shape-dependent quantities of clusters built from spherical nanoparticles. Cluster preparation is accomplished by assembling surface-modified polystyrene particles on evaporating emulsion droplets. This results in supracolloids that exhibit well-defined configurations, which are governed by the number of constituent particles. Sorting into uniform cluster fractions is achieved through centrifugation of the cluster mixture in a density gradient. Sedimentation coefficients are elucidated by differential centrifugal sedimentation. Rotational and translational diffusion of the clusters are investigated by polarized and depolarized dynamic light scattering. The experimental results are compared to data obtained via a bead-shell model suitable for predicting hydrodynamic quantities of particles with arbitrary shapes. The experimental data are in excellent agreement with the predictions from hydrodynamic modeling. The variety of investigated shapes shows the robustness of our approach and provides a complete picture of the hydrodynamic behavior of complex particles.

The non-Gaussian tops and tails of diffusing boomerangs

Experiments involving the two-dimensional passive diffusion of colloidal boomerangs tracked off their centre of mobility have shown striking non-Gaussian tails in their probability distribution function [Chakrabarty et al., Soft Matter, 2016, 12, 4318]. This in turn can lead to anomalous diffusion characteristics, including mean drift. In this paper, we develop a general theoretical explanation for these measurements. The idea relies on calculating the two-dimensional probability densities at the centre of mobility of the particle, where all distributions are Gaussian, and then transforming them to a different reference point. Our model clearly captures the experimental results, without any fitting parameters, and demonstrates that the one-dimensional probability distributions may also exhibit strongly non-Gaussian tops. These results indicate that the choice of tracking point can cause a considerable departure from Gaussian statistics, potentially causing some common modelling techniques to fail.

Advances in the microrheology of complex fluids

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

Effects of translation-rotation coupling on the displacement probability distribution functions of boomerang colloidal particles

Prior studies have shown that low symmetry particles such as micro-boomerangs exhibit behaviour of Brownian motion rather different from that of high symmetry particles because convenient tracking points (TPs) are usually inconsistent with their center of hydrodynamic stress (CoH) where the translational and rotational motions are decoupled. In this paper we study the effects of the translation-rotation coupling on the displacement probability distribution functions (PDFs) of the boomerang colloid particles with symmetric arm length. By tracking the motions of different points on the particle symmetry axis, we show that as the distance between the TP and the CoH is increased, the effects of translation-rotation coupling becomes pronounced, making the short-time 2D PDF for fixed initial orientation to change from elliptical, to bean and then to crescent shape, and the angle averaged PDFs change from ellipsoidal-particle-like PDF to a shape with a Gaussian top and long displacement tails. We also observed that at long times the PDFs revert to Gaussian. These 2D PDF shapes provide a clear physical picture of the non-zero mean displacements observed in boomerangs particles.

The Raspberry model for hydrodynamic interactions revisited. II. The effect of confinement

The so-called "raspberry" model refers to the hybrid lattice-Boltzmann (LB) and Langevin molecular dynamics schemes for simulating the dynamics of suspensions of colloidal particles, originally developed by Lobaskin and Dünweg [New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. In this paper, we present a follow up to our study of the effectiveness of the raspberry model in reproducing hydrodynamic interactions in the Stokes regime for spheres arranged in a simple-cubic crystal [Fischer et al., J. Chem. Phys. 143, 084107 (2015)]. Here, we consider the accuracy with which the raspberry model is able to reproduce such interactions for particles confined between two parallel plates. To this end, we compare our LB simulation results to established theoretical expressions and finite-element calculations. We show that there is a discrepancy between the translational and rotational mobilities when only surface coupling points are used, as also found in Part I of our joint publication. We demonstrate that adding internal coupling points to the raspberry can be used to correct said discrepancy in confining geometries as well. Finally, we show that the raspberry model accurately reproduces hydrodynamic interactions between a spherical colloid and planar walls up to roughly one LB lattice spacing.